Dipole formalism with heavy fermions

TL;DR

The paper extends the Catani-Seymour dipole subtraction formalism to QCD processes involving heavy fermions, deriving the necessary subtraction terms and their analytic integrals in D dimensions while preserving compatibility with conventional dimensional regularization variants. It provides detailed phase-space measures in D dimensions and explicit dipole expressions for all final- and initial-state configurations with massive quarks, enabling the setup of NLO Monte Carlo programs for heavy-quark production. The integration strategy uses parameterizations yielding Beta, hypergeometric, Appell-type integrals and harmonic polylogarithms, facilitating epsilon-expansions to O(epsilon^0). The framework lays the groundwork for higher-order extensions and practical applications such as single-top production, with explicit handling of scheme dependence across CDR, HV, and FD schemes.

Abstract

We extend the dipole formalism of Catani and Seymour to QCD processes involving heavy fermions. We give the appropriate subtraction terms together with their integrated counterpart. All calculations are done within dimensional regularization. Our formulae can be used with three variants of dimensional regularization (conventional dimensional regularization, the 't Hooft-Veltman scheme or the four-dimensional scheme).